Orateur
Description
There has been a surge of interest in recent years in general-purpose
acceleration' methods that take a sequence of vectors converging to the limit
of a fixed point iteration, and produce from it a faster converging sequence. A
prototype of these methods that attracted much attention recently is the
Anderson Acceleration (AA) procedure. We introduce the nonlinear Truncated
Generalized Conjugate Residual (nlTGCR) algorithm, an alternative to AA which is
designed from a careful adaptation of the Conjugate Residual method for solving
linear systems of equations to the nonlinear context. The various links between
nlTGCR and inexact Newton, quasi-Newton, and multisecant methods are exploited
to build a method that has strong global convergence properties and that can
also exploit symmetry when applicable. Taking this algorithm as a starting point
we explore a number of other acceleration procedures including a short-term
(symmetric') version of Anderson Acceleration which we call Anderson
Acceleration with Truncated Gram-Schmidt.
